Dynamics of Induced Systems
Abstract
In this paper we study the dynamical properties of actions on the space of compact subsets of the phase space. More precisely, if is a metric space, let denote the space of non-empty compact subsets of provided with the Hausdorff topology. If is a continuous self-map on , there is a naturally induced continuous self-map on . Our main theme is the interrelation between the dynamics of and . For such a study, it is useful to consider the space of continuous maps from a Cantor set to provided with the topology of uniform convergence, and induced on by composition of maps. We mainly study the properties of transitive points of the induced system both topologically and dynamically, and give some examples. We also look into some more properties of the system.
Recommended Citation
E. Akin et al., "Dynamics of Induced Systems," Ergodic Theory and Dynamical Systems, vol. 37, no. 7, pp. 2034 - 2059, Cambridge University Press, Oct 2017.
The definitive version is available at https://doi.org/10.1017/etds.2016.7
Department(s)
Mathematics and Statistics
International Standard Serial Number (ISSN)
1469-4417; 0143-3857
Document Type
Article - Journal
Document Version
Citation
File Type
text
Language(s)
English
Rights
© 2026 Cambridge University Press, All rights reserved.
Publication Date
01 Oct 2017
